Duo Therm Furnace - lower voltage that triggers blower?

Also sounds like you may have a bad ground. Double check that your furnace has a dedicated negative wire and is not using the camper's skin for its return link.

I had this issue with a Suburban DD16, the negative wire had come unhooked and the unit was using the siding as its return route, which it had a bad ground connection.

On battery, the voltage would drop too much for the furnace to run properly, but it would work fine when on the converter.